An waver means to move back and forth or to have doubts about what to do. You can also waver at something, like a sound that's not steady.
When someone says they're wavering on an important decision, it usually means they're having trouble making up their mind. They might be weighing the pros and cons, and are unsure which way to go. For example, if you've been planning a trip for months but just got a new job offer in a different city, you might start to waver about whether to take the job or stick with your original plans. You could also say that someone's opinions on an issue waver if they're not strong and consistent - like if one day they think something is good, and the next day they think it's bad.
How common is "waver"?
Word waver is considered uncommon in modern English. It appears most frequently in fiction texts and less often in other writings.
Definitions
verb
To swing or wave, especially in the air, wind, etc.; to flutter.
Example: Flowers wavered in the breeze.
To move without purpose or a specified destination; to roam, to wander.
To sway back and forth, as if about to fall; to reel, to stagger, to totter.
To begin to weaken or show signs of weakening in resolve; to falter, to flinch, to give way.
Example: Despite all the terrible things that happened to her, she never wavered from her beliefs.
To feel or show doubt or indecision; to be indecisive between choices; to vacillate.
Of a body part such as an eye or hand, or the voice: to become unsteady; to shake, to tremble.
Example: His voice wavered when the reporter brought up the controversial topic.
Of light, shadow, or a partly obscured thing: to flicker, to glimmer, to quiver.
Chiefly of a quality or thing: to change, to fluctuate, to vary.
Followed by from: to deviate from a course; to stray, to wander.
Of the wits: to become confused or unsteady; to reel.
To cause (someone or something) to move back and forth.
To cause (someone) to begin to or show signs of weakening in resolve; also (rare), to weaken in resolve due to (something).